Estimating large-scale signaling networks through nested effect models with intervention effects from microarray data

Abstract

Motivation: Targeted interventions using RNA interference in combination with the measurement of secondary effects with DNA microarrays can be used to computationally reverse engineer features of upstream non-transcriptional signaling cascades based on the nested structure of effects.

Results: We extend previous work by Markowetz et al., who proposed a statistical framework to score different network hypotheses. Our extensions go in several directions: we show how prior assumptions on the network structure can be incorporated into the scoring scheme by defining appropriate prior distributions on the network structure as well as on hyperparameters. An approach called module networks is introduced to scale up the original approach, which is limited to around 5 genes, to infer large-scale networks of more than 30 genes. Instead of the data discretization step needed in the original framework, we propose the usage of a beta-uniform mixture distribution on the P-value profile, resulting from differential gene expression calculation, to quantify effects. Extensive simulations on artificial data and application of our module network approach to infer the signaling network between 13 genes in the ER-alpha pathway in human MCF-7 breast cancer cells show that our approach gives sensible results. Using a bootstrapping and a jackknife approach, this reconstruction is found to be statistically stable.

Availability: The proposed method is available within the Bioconductor R-package nem.

Fig. 1.

Main idea of the inference framework by Markowetz et al.: a network hypothesis is a directed graph between S-genes. Attached to each S-gene are several E-genes. Knocking down S-gene S₂ interrupts signal flow in the downstream pathway, and hence an effect of E-genes attached to S₂ and to S₁ is expected.

Fig. 2.

Histogram of the P-value distribution of AKT2 knock-down (see Section 3.2). Black: mixture model curve; red: extracted alternative distribution.

Fig. 3.

Basic idea of module networks: by successively moving down the cluster hierarchy we identify the clusters (modules) of S-genes, which are marked in red. They contain 4 S-genes at most and can be estimated by exhaustively searching for the highest scoring model.

Fig. 4.

Simulation results for artificial networks with n = 10, 20 S-genes and varying number of E-genes.

Fig. 5.

Computation times (s) for module networks and triplets inference. For n = 30 triplets inference already becomes impractically slow.

Fig. 6.

Simulation results for artificial networks with n = 30 S-genes and varying number of E-genes (module networks).

Fig. 7.

Average improvement by prior knowledge of 25%, 50%, 75% true posititive and 5% false-positive edges with varying number of E-genes (n = 10 S-genes, module networks).

Fig. 8.

Left: Literature network obtained from Ingenuity™. Right: Consensus network induced by our method (transitively reduced graph).